Synthese

, Volume 135, Issue 3, pp 379–399 | Cite as

The Open-Endedness of the Set Concept and the Semantics of Set Theory

  • A. Paseau
Article

Abstract

Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory.

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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • A. Paseau
    • 1
  1. 1.Trinity CollegeCambridgeU.K. E-mail

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